According to [1]} (see also [2]}, [3]}), an anchored vector bundle \(E\)  with anchor \(\rho \)  is a Courant vector bundle if there is a pseudo-euclidian metric \(g\)  in the fibers of \(E\)  such that \(\rho \circ \#\circ \rho ^{\ast }\colon T^{\ast }M\rightarrow TM\)  vanishes, where \(\#\colon E^{\ast }\rightarrow E\)  is the musical isomorphism induced by \(g\) .
